Seminars "Combinatorics of Vassiliev invariants". Speaker: Mikhail Fedorov

We study embeddings of n-manifolds with a nonempty boundary into R^2n-1.
This problem is interesting, in particular, because there is a similar classification of embeddings of k-connected manifolds with a nonempty boundary, for k>0, which cannot be extended to the case k=0.
We introduce an analogue of the Seifert form for embeddings of punctured n-manifolds into R^2n-1.
We describe some properties of this invariant and restrictions on the set of its possible values. Our main conjecture asserts that this invariant yields a complete classification of embeddings of punctured n-manifolds into R^2n-1.